Algebraic relational semantics for basic substructural logics

This paper addresses one kind of operational (binary and ternary) relational semantics, which we shall call algebraic relational semantics, for basic substructural logics. For this, we first discuss the non-associative and non-commutative substructural logic GL and its axiomatic expansions, their corresponding algebraic structures, and algebraic completeness results. Next, we introduce various types of operational binary relational semantics, called here algebraic Kripke-style semantics, for the substructural logics. Finally, we extend these semantics to ternary relational semantics called here algebraic Routley-Meyer-style semantics.